An average problem in algebra usually involves finding the grade a person needs to make a certain grade in a class. Anytime you know a teacher’s grading system, you can determine your average and find out what kind of grade is needed to make an “A” or a “B”.

Suppose Kirk has taken three tests and made 88, 90, and 84. Kirk’s teacher tells the class that each test counts the same amount. Kirk wants to know what he needs to make on the fourth test to have an overall average of 90 so he can make an A in the class.

The key here is that all the tests count the same. So this is a case where we need to add all four test grades and divide by four. The only problem is, we don’t know the fourth test grade; that’s what we want to find out. So if we call the fourth test grade x, we can add up the four grades and divide by 4. This gives the average of the four test grades. Since we want that average to be 90, we set up the equation as:

We have determined that Kirk needs to make a 98 on the fourth test to get an A. If we check this answer, we get:

Examples

Carla has three test scores of 84, 90, and 86. There is one more test during the semester. She wants to make an A in the class, which means she needs her average to be a 90. All four tests count the same (25% each) in determining the class grade. What grade does she need to make on the fourth test to make an A in the class?

What is your answer?

Allyson has taken four tests and made 82, 77, 75, and 84. She has to take a final exam and her teacher has told her that the final exam will count as two test grades. Allyson really wants to make a B in the class, which means she needs an overall average of 80. What does Allyson need to make on the final to get a B in the class?

What is your answer?

Example Group #2

In this set of examples no hints are provided. Click the soution image once it is revealed to see a step-by-step process to obtain the corrrect answer.

Jim has four test scores of 86, 81, 80, and 75. There is one more test during the semester. He wants to make a B in the class, which means he needs his average to be an 80. All five tests count the same in determining the class grade. What grade does Jim need to make on the fifth test to make a B in the class?

What is your answer?A. 79.5B. 78C. 64.4

Janna has taken three tests and made 92, 77, and 95. She has to take a final exam and her teacher has told her that the final exam will count as two test grades. Janna really wants to make an A in the class, which means she needs an overall average of 90. Janna is not sure if it is possible to make an A since she made a 77 on one of her tests. Is it possible? If not, explain why. If it is possible, what grade does she need to make?